mathematics

Probabilistic risk assessment

Probabilistic risk assessment is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Probabilistic risk assessment rather than just read about it. In short: Probabilistic risk assessment (PRA) is a systematic and comprehensive methodology to evaluate risks associated with a complex engineered technological entity (such as an airliner or a nuclear power plant) or the effects of stressors on the environment (probabilistic environmental risk assessment, or PERA). Risk in a PRA is defined as a feasible detrimental outcome of an activity or action.

Key takeaways

Probabilistic risk assessment belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Probabilistic risk assessment to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Probabilistic risk assessment from memory before moving on to harder problems.

Reference excerpt

Probabilistic risk assessment (PRA) is a systematic and comprehensive methodology to evaluate risks associated with a complex engineered technological entity (such as an airliner or a nuclear power plant) or the effects of stressors on the environment (probabilistic environmental risk assessment, or PERA). Risk in a PRA is defined as a feasible detrimental outcome of an activity or action. In a PRA, risk is characterized by two quantities:

the magnitude (severity) of the possible adverse consequence(s), and the likelihood (probability) of occurrence of each consequence. Consequences are expressed numerically (e.g., the number of people potentially hurt or killed) and their likelihoods of occurrence are expressed as probabilities or frequencies (i.e., the number of occurrences or the probability of occurrence per unit time). The total risk is the expected loss: the sum of the products of the consequences multiplied by their probabilities. The spectrum of risks across classes of events are of concern, and are usually controlled in licensing processes – it would be of concern if rare but high consequence events were found to dominate the overall risk, particularly as these risk assessments are very sensitive to assumptions (how rare is a high consequence event?). Probabilistic risk assessment usually answers three basic questions:

What can go wrong with the studied technological entity or stressor, or what are the initiators or initiating events (undesirable starting events) that lead to adverse consequence(s)? What and how severe are the potential detriments, or the adverse consequences that the technological entity (or the ecological system in the case of a PERA) may be eventually subjected to as a result of the occurrence of the initiator? How likely to occur are these undesirable consequences, or what are their probabilities or frequencies? Two common methods of answering this last question are event tree analysis and fault tree analysis – for explanations of these, see safety engineering. In addition to the above methods, PRA studies require special but often very important analysis tools like human reliability analysis (HRA) and common-cause-failure analysis (CCF). HRA deals with methods for modeling human error while CCF deals with methods for evaluating the effect of inter-system and intra-system dependencies which tend to cause simultaneous failures and thus significant increase in overall risk.

PSA for nuclear power plants One point of possible objection interests the uncertainties associated with a PSA. The PSA (Probabilistic Safety Assessment) has often no associated uncertainty, though in metrology any measure shall be related to a secondary measurement uncertainty, and in the same way any mean frequency number for a random variable shall be examined with the dispersion inside the set of data. For example, without specifying an uncertainty level, the Japanese regulatory body, the Nuclear Safety Commission issued restrictive safety goal in terms of qualitative health objectives in 2003, such that individual fatality risks should not exceed 10−6/year. Then it was translated in a safety goal for nuclear power plants:

for reactors of type BWR-4, in: Core Damage Frequency (CDF): 1.6 × 10−7 /year, Containment Failure Frequency (CFF): 1.2 × 10−8 /yr for reactors of type BWR-5, in: CDF: 2.4 × 10−8 /year, and CFF: 5.5 × 10−9 /yr for The second point is a possible lack of design in order to prevent and mitigate the catastrophic events, which has the lowest probability of the event and biggest magnitude of the impact, and the lowest degree of uncertainty about their magnitude. A cost-effective of the factor of safety, contribute to undervaluate or completely ignore this type of remote safety risk-factors. Designers choose if the system has to be dimensioned and positioned at the mean or for the minimum level of probability-risk (with related costs of safety measures), for being resilient and robust in relation to the fixed value. Such external events may be natural hazard, including earth quake and tsunami, fire, and terrorist attacks, and are treated as a probabilistic argument. Changing historical context shall condition the probability of those events, e.g. a nuclear program or economic sanctions.

Worked examples

Example 1 — a first encounter with Probabilistic risk assessment

Start with the simplest possible case. Write down what Probabilistic risk assessment claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Probabilistic risk assessment before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Probabilistic risk assessment ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Probabilistic risk assessment

In research: Probabilistic risk assessment appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Probabilistic risk assessment in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Probabilistic risk assessment is common in secondary-school and first-year university syllabi. It links to neighbouring topics Probability assessment, Risk analysis methodologies, so understanding it makes those chapters shorter.
In everyday life: Look for Probabilistic risk assessment outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Probabilistic risk assessment in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Probabilistic risk assessment means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Probabilistic risk assessment out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Probabilistic risk assessment in simple terms?

Why does Probabilistic risk assessment matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Probabilistic risk assessment?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Probabilistic risk assessment.